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Thus, it is the partial derivative of the free energy with respect to the amount of the species, all other species' concentrations in the mixture remaining constant. When both temperature and pressure are held constant, and the number of particles is expressed in moles, the chemical potential is the partial molar Gibbs free energy.
This last partial derivative is the same as ¯, the partial molar Gibbs free energy. This means that the partial molar Gibbs free energy and the chemical potential, one of the most important properties in thermodynamics and chemistry, are the same quantity.
The chemical potential is simply another name for the partial molar Gibbs free energy (or the partial Gibbs free energy, depending on whether N is in units of moles or particles).
In thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol ) is a thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure–volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure.
Molar Gibbs free energy is commonly referred to as chemical potential, symbolized by , particularly when discussing a partial molar Gibbs free energy for a component in a mixture. For the characterization of substances or reactions, tables usually report the molar properties referred to a standard state .
In thermodynamics, the fugacity of a real gas is an effective partial pressure which replaces the mechanical partial pressure in an accurate computation of chemical equilibrium. It is equal to the pressure of an ideal gas which has the same temperature and molar Gibbs free energy as the real gas. [1]
[4]: 215 In other words, the temperature, pressure and molar Gibbs free energy are the same between the two phases when they are at equilibrium. An equivalent, more common way to express the vapor–liquid equilibrium condition in a pure system is by using the concept of fugacity. Under this view, equilibrium is described by the following equation:
According to the IUPAC definition, [4] it is the partial molar Gibbs energy of the substance at the specified electric potential, where the substance is in a specified phase. Electrochemical potential can be expressed as